Correlated data are common in biomedical research such as cancer research, where clustered and spatial data are often observed. This correlation may be due to repeated measures over time as in longitudinal studies; or may be due to outcomes from multiple members within the same family as in genetic epidemiology; or may be due to geographic proximity as in estimation of disease maps. Valid statistical analysis needs to account for the correlation among observations. This proposal aims at developing statistical models and methods for several emerging correlated data problems. They include: (1) nonparametric regression which allows flexible modeling of covariate effects using nonparametric spline and kemel techniques, and semiparametric regression where the covariates of main interest are modeled parametrically and the nuisance covariates are modeled nonparametrically; (2) measurement errors in covariates which allow covariates to be measured with errors; (3) case-control studies with longitudinal covariates, where some covariates collected in outcome-dependent retrospective case-control studies are measured longitudinally and retrospectively; (4) causal inference in choice-based longitudinal intervention studies, where a subject chooses which intervention program he/she prefers and causal inference is challenged by the nonrandom nature of the design. Statistical models and methods will be developed to handle these problems and the correlation among observations will be accounted in these statistical developments. Asymptotic properties of the proposed methods will be investigated and simulation studies will be conducted to evaluate their finite sample performance. Efficient numerical algorithms and user-friendly statistical software will be developed, with the goal of disseminating these models and methods to health sciences researchers. In collaboration with biomedical investigators, we will apply the proposed models and methods to several motivating data sets on cancer research and other fields of research.